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    I Pu First Test Aug Dkpucpa

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    darkk62700
    Jjhhyu

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    I Pu First Test Aug Dkpucpa

    Uploaded by

    darkk62700
    5 views2 pages
    Jjhhyu

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    i Pu First Test Aug Dkpucpa (1)

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    Jjhhyu

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    5 views2 pages

    I Pu First Test Aug Dkpucpa

    Uploaded by

    darkk62700
    Jjhhyu

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 2

    DKPUCPA

    FIRST TEST - August – 2023


    FIRST PUC - MATHEMATICS
    Time: 1 hour 30 minutes Max. Marks: 40

    Instructions : The question paper has 4 Parts namely A, B, C and D. Answer all the parts.

    PART-A
    I Answer all the questions 𝟓×𝟏=𝟓
    1. If set A has 3 elements and set B = {3, 4, 5} then the number of elements of A×B is.
    a) 6 b) 3 c) 9 d) 27
    2. The domain of real function 𝑓 defined by f  x   x  1 is given by

    a) R b) [1, ∞) c) (-∞, 1] d) [-1, 1]

    3. If 𝑠𝑖𝑛𝑥 is positive then 𝑥 lies in


    a) I and II quadrant b) I and III quadrant
    c) II and III quadrant d) II and IV quadrant

    4. =

    a) 𝑡𝑎𝑛 +𝑥 b) 𝑡𝑎𝑛 −𝑥 c) 𝑡𝑎𝑛 −𝑥 d) 𝑡𝑎𝑛 +𝑥

    5. The equation of line parallel to x-axis and passing through (2, -3) is
    a) 𝑥 = 2 b) 𝑦 – 3 = 0 c) 𝑦 + 3 = 0 d) 𝑥
    + 𝑦 + 1 = 0

    II Fill in the blanks by choosing the appropriate answer from those given in the bracket. 3 x 1 = 03
    (1, −1, 0) 𝟑×𝟏=𝟑

    6. A function f is defined by 𝑓(𝑥) = 5 – 2𝑥. Write down the value of 𝑓(3) is ________.

    7. If 𝑐𝑜𝑠 + 𝑥 = 0 then one of the value for x is ______.

    8. The slope of the straight line 3x – 3y + 5 = 0 is ________ .

    III Answer the following questions 𝟐×𝟏=𝟐


    9. Write the interval (2, 5] in set builder form .
    10. Convert 120o into radian measure.

    1
    PART-B
    Answer any three questions 𝟑×𝟐=𝟔

    11. If X = {a, e, i, o, u} and Y = {a, i, k, u} find X−Y and Y−X.


    12. If 𝐴 = {1, 2} then find 𝐴 × 𝐴 × 𝐴.
    13. In a circle of diameter 40 c.m the length of a chord is 20 c.m find the length
    of minor arc of the chord.
    14. Prove that 𝑠𝑖𝑛 + 𝑐𝑜𝑠 − 𝑡𝑎𝑛 =−

    15. Find the value of x for which the points (𝑥, −1), (2, 1) 𝑎𝑛𝑑 (4, 5) are collinear .

    PART-C
    Answer any Three questions 𝟑×𝟑=𝟗

    16. If U = {1, 2, 3,4, 5, 6, 7, 8, 9}, 𝐴 = {1, 2, 3, 4, 6} and 𝐵 = { 3, 4, 6, 8}


    then show that (𝐴 ∪ 𝐵)| = 𝐴| ∩ 𝐵 |.
    17. Draw the Venn diagram for (i) 𝐴 ∪ 𝐵 (ii) 𝐴 − 𝐵 (iii) (𝐴 ∩ 𝐵)|
    18. If f(x) = x2 + 1 and g(x) = 2x then find (𝑖) (𝑓 + 𝑔)(𝑥) (𝑖𝑖) (𝑓 – 𝑔)(𝑥) (𝑖𝑖𝑖) (𝑓𝑔)(𝑥)

    19. If 𝑐𝑜𝑠𝑥 = − , 𝑥 lies in the 3rd quadrant, find the values of remaining trigonometric functions.

    20. Prove that cos3x = 4𝑐𝑜𝑠 x− 3𝑐𝑜𝑠𝑥 .

    PART-D
    Answer any Three questions 𝟑 × 𝟓 = 𝟏𝟓

    21. Define identity function draw the graph, write its domain and range.
    22. Define greatest integer function. Draw the graph of it. Also write its domain and range.
    23. Prove geometrically 𝑐𝑜𝑠(𝑥 + 𝑦) = 𝑐𝑜𝑠𝑥𝑐𝑜𝑠𝑦 − 𝑠𝑖𝑛𝑥𝑠𝑖𝑛𝑦.

    24. Prove that = 𝑐𝑜𝑡3𝑥 .

    25. Derive the equation of the straight line having intercepts a and b on x and y axes respectively.
    Hence find the equation of the line cutting off intercepts -3 and 2 on x and y axes respectively.

    **********

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